You don't necessarily have to turn off the game, at least I don't think so. I've had long sessions of play and was pretty sure I went to some walls multiple times within a single session. I thought it was time based.
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Jeff MercadoDec 3 '11 at 17:43

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@JeffMercado In my experience, they don't until you save and quit, regardless of whether you shut down the system, go to the Wii main menu, or go back to the title screen. I say this having played a 14 hour game one day, and in that entire time, the Goddess Wall directly outside the Sealed Temple didn't respawn.
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user2974Dec 3 '11 at 17:59

I can confirm what Powerlord said. Just tried it. Simply saving and quitting resets the walls.
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user15806Dec 3 '11 at 20:23